Ptolemy Scientific Research Press (PSR Press)is a highly regarded publisher of scientific literature dedicated to bringing the latest research and findings to a broader audience. With a focus on cutting-edge research and technology, Ptolemy Scientific Research Press offers a range of publications catering to professionals, researchers, and student’s needs. Whether looking for information on the latest breakthroughs in physics, biology, engineering, or computer science, you can trust Ptolemy Scientific Research Press to deliver insightful, accurate, and engaging content. With its commitment to quality, accessibility, and innovation, Ptolemy Scientific Research Press is an essential resource for anyone interested in science and technology.
Latest Published Articles
OMS-Vol. 2 (2018), Issue 1, pp. 307–322 Open Access Full-Text PDF
Merve Zingil, Fatma Serap Topal
Abstract:The main goal of this article is to study the oscillation criteria of the second-order neutral differential equations on time scales. We give several theorems and related examples to illustrate the applicability of these theorems. Our results extend some recent work in the literature.
Remarks on Fractional Locally Harmonious Coloring
OMS-Vol. 2 (2018), Issue 1, pp. 301–306 Open Access Full-Text PDF
Wei Gao
Abstract:Locally harmonious coloring is a relax version of standard harmonious coloring which only needs that the color pairs for adjacent edges are different. In this remark, we introduce the concept of fractional locally harmonious coloring, and present some basic facts for this coloring.
Necessary and sufficient condition for a surface to be a sphere
OMA-Vol. 2 (2018), Issue 2, pp. 51–52 | Open Access Full-Text PDF
Alexander G. Ramm
Abstract:Let \(S\) be a \(C^{1}\)-smooth closed connected surface in \(\mathbb{R}^3\), the boundary of the domain \(D\), \(N=N_s\) be the unit outer normal to \(S\) at the point \(s\), \(P\) be the normal section of \(D\). A normal section is the intersection of \(D\) and the plane containing \(N\). It is proved that if all the normal sections for a fixed \(N\) are discs, then \(S\) is a sphere. The converse statement is trivial.
Topological degrees on unbounded domains
OMA-Vol. 2 (2018), Issue 2, pp. 41–50 | Open Access Full-Text PDF
Dhruba R. Adhikari, Ishwari J. Kunwar
Abstract:Let \(D\) be an open subset of \(\mathbf R^N\) and \(f: \overline D\to \mathbf R^N\) a continuous function. The classical topological degree for \(f\) demands that \(D\) be bounded. The boundedness of domains is also assumed for the topological degrees for compact displacements of the identity and for operators of monotone type in Banach spaces. In this work, we follow the methodology introduced by Nagumo for constructing topological degrees for functions on unbounded domains in finite dimensions and define the degrees for Leray-Schauder operators and \((S_+)\)-operators on unbounded domains in infinite dimensions.
Analytical Technique for (2+1) Fractional Diffusion Equation with Nonlocal Boundary Conditions
OMS-Vol. 2 (2018), Issue 1, pp. 287–300 Open Access Full-Text PDF
Rahmatullah Ibrahim Nuruddeen, Bashir Danladi Garba
Abstract:In the present article, a time fractional diffusion problem is formulated with special boundary conditions, specifically the nonlocal boundary conditions. This new problem is then solved by utilizing the Laplace transform method coupled to the well-known Adomian decomposition method after employing the modified version of Beilin’s lemma featuring fractional derivative in time. The Caputo fractional derivative is used. Some test problems are included.
Analytic Functions of Complex Order Defined by New Differential Operator
OMS-Vol. 2 (2018), Issue 1, pp. 266–286 Open Access Full-Text PDF
Abdussalam Eghbiq, Maslina Darus
Abstract:In this paper, we introduce and study the classes \(S_{n,\mu}(\gamma,\alpha,\beta,\) \(\lambda,\nu,\varrho,\mho)\) and \(R_{n,\mu}(\gamma,\alpha,\beta,\lambda,\nu,\varrho,\mho)\) of functions \(f\in A(n)\) with \((\mu)z(D^{\mho+2}_{\lambda,\nu,\varrho}(\alpha,\omega)f(z))^{‘} \) \(+(1-\mu)z(D^{\mho+1}_{\lambda,\nu,\varrho}(\alpha,\omega)f(z))^{‘}\neq0\), where \(\nu>0,\varrho,\omega,\lambda,\alpha,\mu \geq0, \mho\in N_{0}, z\in U\) and \(D^{\mho}_{\lambda,\nu,\varrho}(\alpha,\omega)f(z):A(n)\longrightarrow A(n),\) is the linear differential operator, newly defined as
\( D^{\mho}_{\lambda,\nu,\varrho}(\alpha,\omega)f(z)=z-\sum_{k=n}^{\infty}\left( \dfrac{\nu+k(\varrho+\lambda)\omega^{\alpha}}{\nu} \right)^{\mho} a_{k+1}z^{k+1}. \)
Several properties such as coefficient estimates, growth and distortion theorems, extreme points, integral means inequalities and inclusion relation for the functions included in the classes \(S_{n,\mu} (\gamma,\alpha,\beta,\lambda,\nu,\varrho,\mho,\omega)\) and \(R_{n,\mu}(\gamma,\alpha,\beta,\lambda,\nu,\varrho,\mho,\omega)\) are given.
\( D^{\mho}_{\lambda,\nu,\varrho}(\alpha,\omega)f(z)=z-\sum_{k=n}^{\infty}\left( \dfrac{\nu+k(\varrho+\lambda)\omega^{\alpha}}{\nu} \right)^{\mho} a_{k+1}z^{k+1}. \)
Several properties such as coefficient estimates, growth and distortion theorems, extreme points, integral means inequalities and inclusion relation for the functions included in the classes \(S_{n,\mu} (\gamma,\alpha,\beta,\lambda,\nu,\varrho,\mho,\omega)\) and \(R_{n,\mu}(\gamma,\alpha,\beta,\lambda,\nu,\varrho,\mho,\omega)\) are given.